In a large, 6 qt soup pot or larger, melt butter. Add the carrots, celery, onions, and seasonings. Cook until fragrant, about 3-5 minutes. Add the all purpose flour.
Stir in the broth, 1 cup water, wild rice, thyme, chopped rosemary. Bring to light boil/simmer. Once boiling, cover and reduce the heat to low, cook 30-40 minutes, until the rice is tender.
Add the cooked, shredded chicken and milk. Add ½ cup more water or milk if you'd like to thin the soup at all. Simmer for another 3-5 minutes.
Add the ripped kale or spinach, fresh squeeze lemon juice and parmesan. Take it off the heat.
Serve and garnish generously with extra parmesan. Enjoy!